{
  "id": "2105.11371",
  "version": "v1",
  "published": "2021-05-24T16:03:34.000Z",
  "updated": "2021-05-24T16:03:34.000Z",
  "title": "On the pathwidth of hyperbolic 3-manifolds",
  "authors": [
    "Kristóf Huszár"
  ],
  "comment": "21 pages, 13 figures",
  "categories": [
    "math.GT",
    "cs.CG"
  ],
  "abstract": "According to Mostow's celebrated rigidity theorem, the geometry of closed hyperbolic 3-manifolds is already determined by their topology. In particular, the volume of such manifolds is a topological invariant and, as such, has been investigated for half a century. Motivated by the algorithmic study of 3-manifolds, Maria and Purcell have recently shown that every closed hyperbolic 3-manifold M with volume vol(M) admits a triangulation with dual graph of treewidth at most C vol(M), for some universal constant C. Here we improve on this result by showing that the volume provides a linear upper bound even on the pathwidth of the dual graph of some triangulation, which can potentially be much larger than the treewidth. Our proof relies on a synthesis of tools from 3-manifold theory: generalized Heegaard splittings, amalgamations, and the thick-thin decomposition of hyperbolic 3-manifolds. We provide an illustrated exposition of this toolbox and also discuss the algorithmic consequences of the result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-24T16:03:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q15",
      "57N10",
      "05C75",
      "57M15",
      "F.2.2",
      "G.2.2"
    ],
    "keywords": [
      "dual graph",
      "mostows celebrated rigidity theorem",
      "closed hyperbolic",
      "linear upper bound",
      "algorithmic study"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}